flat rate charge for iPhone screen repair for iphone 6s plus

This is the chart for the US.

iPhone screen replacement costs

The repair pricing in this chart applies only to screen damage. If you have any other damage to your iPhone, you’ll pay additional costs.

The only difference would be between having Apple Care + or not. That is not an estimate.

Where are you located? I know the United States price list was provided, but I understand that a lot of people posting here aren't in the United States where these prices apply.

In many countries where Apple doesn't directly provide service, the cost of a repair is up to that of the authorized service provider. Many will charge hourly repair rates in addition to their charge for the glass. Also - repairs from Apple Authorized Service Providers may still be different than what Apple would charge in markets where Apple will directly service devices (through Apple Stores or mail-in).